Question 4.19: Graph log(x) and ln(x) on the same diagram for −1 < x &lt......

Calculate a table of values for each function, using your calculator to evaluate the logs or, better still, use Excel. No real value exists for the logs of zero (doesn’t exist) or logs of negative numbers (complex). This is indicated on the calculator by – E – and in Excel by #NUM!. Table 4.15 outlines the points used to plot the graphs in Figure 4.20. From Figure 4.20, some properties of log functions can be deduced:

•  There are no real logs of negative numbers.
•  Logs of numbers less than one are negative.
•  log(1) = 0 for any base.
•  logs of numbers greater than one are always positive.

In addition, the graph of \log_{e}(x) is steeper, that is, it increases and decreases more rapidly than \log_{10}(x).